Induction by a Hilbert hypercube representation

This thesis describes a novel connectionist machine utilizing induction by a Hilbert hypercube representation. This representation offers a number of distinct advantages which are described. We construct a theoretical and practical learning machine which lies in an area of overlap between three disciplines - neural nets, machine learning and knowledge acquisition - hence it is refered to as a "coalesced" machine. To this unifying aspect is added the various advantages of its orthogonal lattice structure as against less structured nets. We discuss the case for such a fundamental and low level empirical learning tool and the assumptions behind the machine are clearly outlined. Our theory of an orthogonal lattice structure the Hilbert hypercube of an n-dimensional space using a complemented distributed lattice as a basis for supervised learning is derived from first principles on clearly laid out scientific principles. The resulting "subhypercube theory" was implemented in a development machine which was then used to test the theoretical predictions again under strict scientific guidelines. The scope, advantages and limitations of this machine were tested in a series of experiments. Novel and seminal properties of the machine include: the "metrical", deterministic and global nature of its search; complete convergence invariably producing minimum polynomial solutions for both disjuncts and conjuncts even with moderate levels of noise present; a learning engine which is mathematically analysable in depth based upon the "complexity range" of the function concerned; a strong bias towards the simplest possible globally (rather than locally) derived "balanced" explanation of the data; the ability to cope with variables in the network; and new ways of reducing the exponential explosion. Performance issues were addressed and comparative studies with other learning machines indicates that our novel approach has definite value and should be further researched.

A generative probabilistic oriented wavelet model for texture segmentation

This Letter addresses image segmentation via a generative model approach. A Bayesian network (BNT) in the space of dyadic wavelet transform coefficients is introduced to model texture images. The model is similar to a Hidden Markov model (HMM), but with non-stationary transitive conditional probability distributions. It is composed of discrete hidden variables and observable Gaussian outputs for wavelet coefficients. In particular, the Gabor wavelet transform is considered. The introduced model is compared with the simplest joint Gaussian probabilistic model for Gabor wavelet coefficients for several textures from the Brodatz album [1]. The comparison is based on cross-validation and includes probabilistic model ensembles instead of single models. In addition, the robustness of the models to cope with additive Gaussian noise is investigated. We further study the feasibility of the introduced generative model for image segmentation in the novelty detection framework [2]. Two examples are considered: (i) sea surface pollution detection from intensity images and (ii) image segmentation of the still images with varying illumination across the scene.